{"id":"https://openalex.org/W4411498669","doi":"https://doi.org/10.1142/s2810939225400027","title":"Murmurations and Sato\u2013Tate conjecture for high rank zetas of elliptic curves II: Beyond Riemann hypothesis","display_name":"Murmurations and Sato\u2013Tate conjecture for high rank zetas of elliptic curves II: Beyond Riemann hypothesis","publication_year":2025,"publication_date":"2025-06-20","ids":{"openalex":"https://openalex.org/W4411498669","doi":"https://doi.org/10.1142/s2810939225400027"},"language":"en","primary_location":{"id":"doi:10.1142/s2810939225400027","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s2810939225400027","pdf_url":null,"source":{"id":"https://openalex.org/S4387280190","display_name":"International Journal of Data Science in the Mathematical Sciences","issn_l":"2810-9392","issn":["2810-9392","2810-9406"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319815","host_organization_name":"World Scientific","host_organization_lineage":["https://openalex.org/P4310319815"],"host_organization_lineage_names":["World Scientific"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Data Science in the Mathematical Sciences","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5101037636","display_name":"Zhan Shi","orcid":null},"institutions":[{"id":"https://openalex.org/I135598925","display_name":"Kyushu University","ror":"https://ror.org/00p4k0j84","country_code":"JP","type":"education","lineage":["https://openalex.org/I135598925"]}],"countries":["JP"],"is_corresponding":false,"raw_author_name":"Zhan Shi","raw_affiliation_strings":["Graduate Program of Mathematics for Innovation, Kyushu University, Fukuoka, Japan"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Graduate Program of Mathematics for Innovation, Kyushu University, Fukuoka, Japan","institution_ids":["https://openalex.org/I135598925"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5068435324","display_name":"Lin Weng","orcid":null},"institutions":[{"id":"https://openalex.org/I135598925","display_name":"Kyushu University","ror":"https://ror.org/00p4k0j84","country_code":"JP","type":"education","lineage":["https://openalex.org/I135598925"]}],"countries":["JP"],"is_corresponding":true,"raw_author_name":"Lin Weng","raw_affiliation_strings":["Faculty of Mathematics, Kyushu University, Fukuoka, Japan"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Faculty of Mathematics, Kyushu University, Fukuoka, Japan","institution_ids":["https://openalex.org/I135598925"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5068435324"],"corresponding_institution_ids":["https://openalex.org/I135598925"],"apc_list":null,"apc_paid":null,"fwci":3.4776,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":{"value":0.89688362,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":91,"max":95},"biblio":{"volume":"03","issue":"02","first_page":"45","last_page":"61"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10061","display_name":"Algebraic Geometry and Number Theory","score":0.9911999702453613,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10061","display_name":"Algebraic Geometry and Number Theory","score":0.9911999702453613,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T13802","display_name":"Vietnamese History and Culture Studies","score":0.9846000075340271,"subfield":{"id":"https://openalex.org/subfields/3312","display_name":"Sociology and Political Science"},"field":{"id":"https://openalex.org/fields/33","display_name":"Social Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},{"id":"https://openalex.org/T11166","display_name":"Analytic Number Theory Research","score":0.9836000204086304,"subfield":{"id":"https://openalex.org/subfields/2602","display_name":"Algebra and Number Theory"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/conjecture","display_name":"Conjecture","score":0.7376558184623718},{"id":"https://openalex.org/keywords/riemann-hypothesis","display_name":"Riemann hypothesis","score":0.7216062545776367},{"id":"https://openalex.org/keywords/rank","display_name":"Rank (graph theory)","score":0.660280168056488},{"id":"https://openalex.org/keywords/elliptic-curve","display_name":"Elliptic curve","score":0.6038359999656677},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5820895433425903},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.4130403399467468},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.36836886405944824}],"concepts":[{"id":"https://openalex.org/C2780990831","wikidata":"https://www.wikidata.org/wiki/Q319141","display_name":"Conjecture","level":2,"score":0.7376558184623718},{"id":"https://openalex.org/C199479865","wikidata":"https://www.wikidata.org/wiki/Q205966","display_name":"Riemann hypothesis","level":2,"score":0.7216062545776367},{"id":"https://openalex.org/C164226766","wikidata":"https://www.wikidata.org/wiki/Q7293202","display_name":"Rank (graph theory)","level":2,"score":0.660280168056488},{"id":"https://openalex.org/C179603306","wikidata":"https://www.wikidata.org/wiki/Q268493","display_name":"Elliptic curve","level":2,"score":0.6038359999656677},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5820895433425903},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.4130403399467468},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.36836886405944824}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1142/s2810939225400027","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s2810939225400027","pdf_url":null,"source":{"id":"https://openalex.org/S4387280190","display_name":"International Journal of Data Science in the Mathematical Sciences","issn_l":"2810-9392","issn":["2810-9392","2810-9406"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319815","host_organization_name":"World Scientific","host_organization_lineage":["https://openalex.org/P4310319815"],"host_organization_lineage_names":["World Scientific"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Data Science in the Mathematical Sciences","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/10","display_name":"Reduced inequalities","score":0.44999998807907104}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":10,"referenced_works":["https://openalex.org/W2016397025","https://openalex.org/W2040403535","https://openalex.org/W2061866950","https://openalex.org/W2161444209","https://openalex.org/W2746305147","https://openalex.org/W3007628986","https://openalex.org/W3010079137","https://openalex.org/W3021607650","https://openalex.org/W4244408541","https://openalex.org/W4411498669"],"related_works":["https://openalex.org/W4391375266","https://openalex.org/W4300899577","https://openalex.org/W3194471551","https://openalex.org/W2951225764","https://openalex.org/W4389775313","https://openalex.org/W118970476","https://openalex.org/W2513246935","https://openalex.org/W1944395271","https://openalex.org/W1888039291","https://openalex.org/W2336546597"],"abstract_inverted_index":{"As":[0],"a":[1,27,73,77],"continuation":[2],"of":[3,20,39,80,92,128,188],"our":[4,142],"earlier":[5,85],"paper":[6,94,144],"[Z.":[7],"Shi":[8],"and":[9,13,32,88,98,165],"L.":[10],"Weng,":[11],"Murmurations":[12],"Sato\u2013Tate":[14,33,69,160],"conjectures":[15],"for":[16,35,52,67,105,185],"high":[17],"rank":[18,37,62,102,118,130,156,166],"zetas":[19,38,187],"elliptic":[21,40,106,189],"curves,":[22,107],"preprint,":[23],"arXiv:2410.04952],":[24],"we":[25,147],"offer":[26],"new":[28],"approach":[29,43],"to":[30,177],"murmurations":[31,170],"laws":[34],"higher":[36],"curves.":[41,190],"Our":[42],"here":[44],"does":[45],"not":[46],"depend":[47],"on":[48,72,140],"the":[49,53,68,89,117,129,149,178,182],"Riemann":[50,122,134],"hypothesis":[51,123,135],"so-called":[54],"[Formula:":[55,58,63,119,131,137,152,157,167],"see":[56,59,64,120,132,138,153,158,168],"text]-invariant":[57],"text]":[60,65,121,133,139,159,169],"in":[61,95,181],"even":[66],"law,":[70],"rather,":[71],"much":[74],"refined":[75],"structure,":[76],"similar":[78,176],"version":[79],"which":[81,141],"was":[82,124],"already":[83],"observed":[84],"by":[86],"Zagier":[87],"senior":[90],"author":[91],"this":[93],"[L.":[96],"Weng":[97],"D.":[99],"Zagier,":[100],"Higher":[101],"zeta":[103],"functions":[104],"Proc.":[108],"Natl.":[109],"Acad.":[110],"Sci":[111],"USA":[112],"117(9)":[113],"(2020)":[114],"4546\u20134558]":[115],"when":[116],"established.":[125],"Namely,":[126],"instead":[127],"bounds":[136,151],"first":[143],"is":[145],"based,":[146],"use":[148],"asymptotic":[150],"text].":[154],"Accordingly,":[155],"law":[161],"can":[162,171],"be":[163,172],"established":[164],"formulated":[173],"equally":[174],"well,":[175],"corresponding":[179],"structures":[180],"abelian":[183],"framework":[184],"Artin":[186]},"counts_by_year":[{"year":2025,"cited_by_count":1}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}